Given f(x) = the quantity of x plus 4, divided by 6, solve for f−1(7).

F(x) = (x + 4)/6

find f⁻¹(7)

so, the first thing you need to do here is find f⁻¹, period. this is the notation for the inverse of a function, so you need to start out by finding the inverse of your given function. the inverse is found by swapping your x and y variables, then solving for y.

f(x) = (x + 4)/6  ... change f(x) to y
y = (x + 4)/6 ... swap x and y
x = (y + 4)/6 ... solve for y, start by multiplying both sides by 6 to cancel out your denominator
6x = y + 4 ... subtract 4
6x - 4 = y ... this is your inverse function

if y = 6x - 4 is your inverse function, the last thing you need to do is plug in 7 for x to get the value your question asked for:

f⁻¹(7) = 6(7) - 4
f⁻¹(7) = 42 - 4
f⁻¹(7) = 38